Topological insulators are unique physical structures that in their bulk, but support currents at edges which can be unidirectional and topologically protected from scattering on disorder inhomogeneities. Photonic topological crafted materials exhibit a strong nonlinear response, thus opening the door to exploration of interplay between nonlinearity effects. Among fascinating new phenomena aris...

The Floquet–based quantum–classical Liouville equation (F–QCLE) is presented as a novel theoretical model for the interaction of molecules with intense laser pulses. This equation efficiently combines the following two approaches: First, a small but spectroscopically relevant part of the molecule is treated quantum–mechanically while the remaining degrees of freedom are modelled by means of cla...

Introduction Photonic crystal is a periodic structure consisting of high contrast dielectrics, in which the electromagnetic wave cannot transmit in a specific wavelength range. It is therefore known that, if localized defects are introduced in the photonic crystal, the electromagnetic fields are strongly confined around the defects. For example, point defects in the photonic crystal work as res...

Neural mass models are ubiquitous in large scale brain modelling. At the node level they are written in terms of a set of ODEs with a nonlinearity that is typically a sigmoidal shape. Using structural data from brain atlases they may be connected into a network to investigate the emergence of functional dynamic states, such as synchrony. With the simple restriction of the classic sigmoidal nonl...

The unique conduction properties of condensed matter systems with topological order have recently inspired a quest for the similar effects in classical wave phenomena. Acoustic topological insulators, in particular, hold the promise to revolutionize our ability to control sound, allowing for large isolation in the bulk and broadband one-way transport along their edges, with topological immunity...

By a straightforward generalisation, we extend the work of Combescure [J. Stat. Phys. 59, 679 (1990)] from rank-1 to rank-N perturbations. The requirement for the Floquet operator to be pure point is established and compared to that in Combescure. The result matches that in McCaw and McKellar [J. Math. Phys. 46, 032108 (2005)]. The method here is an alternative to that work. We show that if the...